Barry moved to Goodison Park on loan from Manchester City on transfer deadline day and has impressed for Roberto Martinez's side.
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His debut against Chelsea saw Everton collect all three points, and a last-gasp tackle from the 32-year-old helped deny Samuel Eto'o as they secured the win.
The midfielder has not played for England since May 2012 when he replaced Steven Gerrard at half-time in the 1-0 win over Norway in Oslo.
Everton team-mates Leon Osman and Ross Barkley have since represented England in midfield but Barry still believes that he has something to offer Roy Hodgson.
"It's [a call-up] something that I definitely wouldn't be turning down at the moment," he told the club's official website.
"I joined Everton to play regular football and that's still my main target, to get my form going.
"If an England call comes with that, then fantastic. But it's certainly at the back of my mind.
"I'm looking at keeping a good run of form going and helping Everton climb the table to see where it gets us."
Barry was ineligible for Everton's only Premier League defeat of the season against his parent club Manchester City, but he will be ready to return for the visit of Hull City after the international break.